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Find the sum of the following APs. (i) 2, 7, 12 ,…., to 10 terms. (ii) − 37, − 33, − 29 ,…, to 12 terms (iii) 0.6, 1.7, 2.8 ,…….., to 100 terms (iv) 1/15, 1/12, 1/10,………, to 11 terms

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A basic and conceptual question from arithmetic progression chapter in which we are to find the sum of each of following APs:

(i) 2, 7, 12 ,…., to 10 terms.

(ii) − 37, − 33, − 29 ,…, to 12 terms (iii) 0.6, 1.7, 2.8 ,…….., to 100 terms (iv) 1/15, 1/12, 1/10,………, to 11 terms.

Book – RS Aggarwal, Class 10, chapter 5C,  question no 1.

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1. (i) 2,7,12…… to 10th term

Here a=2,n=10

And d=72=5

Sn=n/2[2a+(n1)d]

S10=10/2[2(2)+(101)5]=5(4+9×5)=245

(ii) 37,33,29,........ to 12th term

Here a=37,n=12

And d=3337=4

Sn=n/2[2a+(n1)d]

S12=12/2[2(37)+(121)(4]=6(7411×4)=180

(iii) 0.6,1.7,2.8............ to 100 term

Here a=0.6,n=100

And d=1.70.6=1.1

Sn=n/2[2a+(n1)d]

S100=100/2[2(0.6)+(1001)(1.1)]
=50(1.299×1.1)
=5505

(iv)151,121,101....... to 11th term

a=151n=11

d=1/12−1/15=(54)/60=1/60

S11=11/2[2(1/15+(111)1/60)]

= 11​/2(2/15+10​/60)

= 11/2×9​/30=33/20

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